Drawing Phylogenetic Networks

1. Drawing Phylogenetic Networks Daniel H. Huson joint work with Tobias Kloepper and Regula Rupp Future Directions in Phylogenetics, Cambridge, December 2007

2. Split Networks and Cluster Networks Split network Cluster network Data: binary sequences (Kumar, 1998)

3. How to Draw Cluster Networks? Data: 61 genes (Leebens-Mack et al, MBE, 2005)

4. Cladograms For Trees

5. Phylograms and Radial Diagrams

6. Drawing a Cladogram for a Tree 0 Assign x-coords in a postorder traversal of N: if v is a leaf: x(v) = 0 else: x(v) = max x of children + 1 1 0 3 0 2 0 4 1 0 0

7. Drawing a Cladogram for a Tree 1 Assign y-coords in a postorder traversal: if v is a leaf: y(v) = number of leaves visited else: y(v) = mean y of children 1.5 2 2.625 3 3.75 4 4.125 4.5 5 6

8. Naïve Algorithm for Drawing Networks Network N: • Choose a guide tree T • Compute coordinates for T • Draw network using tree coordinates q p p

9. Naïve Algorithm for Drawing Networks Problems: • x-coordinates: P and Q have different x-coordinates • y-coordinates: R isn‘t placed between P and Q • Unnecessary edge crossings R Q P

10. Better x-Coordinates Assign x-coords in a postorder traversal of N: if v is a leaf: x(v) = 0 else: x(v) = max x of children + 1 0 1 2 0 1 0 4 0 3 0 2

11. Better y-Coordinates? • Need to introduce: • LSA guide tree • topological embedding 

12. Lowest Single Ancestor • The LSA of a node v is the last node ( v) on all paths from  to v: v  lsa(v)

13. LSA Guide Tree • Connect each reticulate node to its LSA and remove all reticulate edges: LSA tree T cladogram

14. Topological Embedding • A topological embedding is given by an ordering of the children of each node v: • Any  gives rise to a planar drawing of T v e q v d r q r  r w b p p w a

15. Better y-Coordinates • Choose  so that reticulate nodes are placed between their sources: • Order subtrees in preorder traversal of T

16. Resulting Cladogram • Use diagonal or curved lines for reticulate edges

17. Additional Twist for y-Coordinates • LSA guide tree has true and false leaves: Network N LSA tree T • A leaf is false if it is only a leaf in T

18. Additional Twist for y-Coordinates • False leaves produce uneven spacing of leaves in N:

19. 1 2 3 3½ 4 5 6 Additional Twist for y-Coordinates • Assign integer coordinates to true leaves, fractional to false ones:

20. Circular Cladograms • Compute polar coordinates in similar way:

21. Phylograms and Radial Diagrams • y-coordinates: as for cladogram • x-coordinates: preorder traversal

22. Example 1 • Multiple gene trees • Leebens-Mack et al, MBE, 2005 • 61 chloroplast genes for 26 plants • Filtered cluster networks • 50% • 30% • 20% • 10%

23. Example 2: Splits vs Clusters Split network of consensus splits from 106 maximum-parsimony trees (Rokas et al, 2003) (Holland et al, 2004) Weighted cluster network

24. Weights for Reticulate Edges? • Use LSA to determine weight of reticulate edge: • Use average weight on paths to lsa(v) 1,2,3,4,5 1,3,4 v  lsa(v) 2,5

25. Example 3 • Arndt von Haeseler • over 12,000 trees • 76.5 % • 11.4 % • 11.4 % Weighted cluster network

26. Outlook • All algorithms discussed have been implemented and will be made available in Dendroscope2 • Dendroscope2 will be released in first half of 2008 • Dendroscope 1 (for trees only) is available from: www-ab.informatik.uni-tuebingen.de/software